Micromagnetic modelling allows the systematic study of the effects of particle size and shape on the first-order reversal curve (FORC) magnetic hysteresis response for magnetite particles in the single-domain (SD) and pseudo-single domain (PSD) particle size range. The interpretation of FORCs, though widely used, has been highly subjective.  Here, we use micromagnetics to model randomly oriented distributions of particles to allow more physically meaningful interpretations.  We show that one commonly found type of PSD particle - namely single vortex (SV) particles - has far more complex signals than SD particles, with multiple peaks and troughs in the FORC distribution, where the peaks have higher switching fields for larger SV particles. Particles in the SD to SV transition zone have the lowest switching fields. Symmetrical and prolate particles display similar behavior, with distinctive peaks forming near the vertical axis of the FORC diagram. In contrast, highly oblate particles produce `butterfly' structures, suggesting that these are potentially diagnostic of particle morphology. We also consider FORC diagrams for distributions of particle sizes and shapes and produce an online application that users can use to build their own FORC distributions.  There is good agreement between the model predictions for distributions of particle sizes and shapes, and the published experimental literature.

Paleointensity observations from meteorites provide insights into planetary formation and evolution. Meteoritic samples are usually dominated by Fe-rich kamacite, which is capable of faithfully recording the ancient dynamo activity of meteorites’ parent body. To retrieve paleointensity estimates, experimental protocols assume that samples are dominated by uniformly magnetized particles. However, most magnetic carriers observed in extraterrestrial samples are non-uniformly magnetized. This inconsistency represents a major impediment in reliably reconstructing paleointensities from meteorites. Here we present the State Group Algorithm (SGA); a micromagnetic based model capable of efficiently simulating thermoremance acquisition of magnetic particles with a single-vortex domain state. The results show that iron particles can acquire thermoremance that is linear with the external field up to ∼100 µT. Single-vortex cooling rate effects are generally weaker than those of single-domain particles, providing more accurate paleointensity estimates. A small number of particles exhibit inverse cooling rate effects, leading to underestimates in paleointensity.

Magnetic hysteresis measurements are routinely made in the Earth and planetary sciences to identify geologically meaningful  magnetic recorders, and to study variations in present and past environments. Interpreting magnetic hysteresis data in terms of domain state (particle size)  and paleomagnetic stability are major motivations behind undertaking these measurements, but the interpretations remain  fraught with challenges and ambiguities.To shed new light on these ambiguities, we have undertaken a systematic micromagnetic study to quantify the magnetic hysteresis behavior of room-temperature magnetite as a function of particle size (50-195 nm; equivalent spherical volume diameter) and shape (oblate, prolate and equant);our models span uniformly magnetized single domain (SD) to non-uniformly magnetized single vortex (SV) states.Within our models the reduced magnetization  marks a clear boundary between SD (≥0.5) and SV (<0.5) magnetite.We further identify particle sizes and shapes with unexpectedly low coercivity and coercivity of remanence. These low coercivity regions correspond to magnetite particles that typically have multiple possible magnetic domain states, which has been previously linked to a zone of unstable magnetic recorders.Of all hysteresis parameters investigated, transient hysteresis is most sensitive to particles that exhibit such domain state multiplicity, leading us to suggest that transient behavior be more routinely measured during rock magnetic investigations.

First-order reversal curve (FORC) diagrams are a standard rock magnetic tool for analyzing bulk magnetic hysteresis behaviors, which are used to estimate the magnetic mineralogies and magnetic domain states of grains within natural materials. However, the interpretation of FORC distributions is challenging due to complex domain-state responses, which introduce well-documented uncertainties and subjectivity. Here, we propose a neural network algorithm (FORCINN) to invert the size and aspect ratio distribution from measured FORC data. We trained and tested the FORCINN model using a dataset of synthetic numerical FORCs for single magnetite grains with various grain-sizes (45-400 nm) and aspect ratios (oblate and prolate grains). In addition to successfully testing FORCINN against synthetic datasets, we also tested FORCINN against FORC data measured on natural samples with accurately determined grain-size and aspect ratio distributions. FORCINN was found to provide good estimates of the grain-size distributions for basalt samples and marine sediments.

The cloudy zone (CZ), a nm-sized intergrowth of taenite or tetrataenite crystals (or islands), is the most promising phase to preserve palaeomagnetic records in (stony-)iron meteorites. While slowly-cooled meteorites form tetrataenite – an extremely good recorder – fast-cooled meteorites contain fine-grained taenite islands, which were considered unsuitable for palaeomagnetic studies. In this work, however, we show that nm-sized taenite grains are stable over billion-year timescales, indicating that taenite-bearing meteorites are reliable sources of paleomagnetic information. Additionally, we find a range of sizes for which taenite forms stable single-domain structures. Single-domain states might be preserved even through subsequent tetrataenite ordering, implying that tetrataenite might carry magnetization state inherited from its precursor taenite. This remanent magnetization can be up to 10\textsuperscript{5} years older than that of larger tetrataenite islands in the same meteorite, which would have been reset upon ordering. This allow studding to two distinct events of planetesimal formation from a single sample.

The minerals carrying the magnetic remanence in geological samples are commonly a solid solution series of iron-titanium spinels known as titanomagnetites. Despite the range of compositions within this series, micromagnetic studies that characterize the magnetic domain structures present in these minerals have typically focused on magnetite. No studies systematically comparing the domain-states present in titanomagnetites have been undertaken since the discovery of the single vortex (SV) structure and the advent of modern micromagnetism. The magnetic properties of the titanomagnetite series are known to vary with composition, which may influence the domain states present in these minerals, and therefore the magnetic stability of the samples bearing them. We present results from micromagnetic simulations of titanomagnetite ellipsoids of varying shape and composition to find the size ranges of the single domain (SD) and SV structures. These size ranges overlap, allowing for regions where the SD and SV structures are both available. These regions are of interest as they may lead to magnetic instability and “pTRM tails’ in paleointensity experiments. We find that although this SD+SV zone occupies a narrow range of sizes for equidimensional magnetite, it is widest for intermediate (TM30-40) titanomagnetite compositions, and increases for both oblate and prolate particles, with some compositions and sizes having an SD+SV zone up to 100s of nm wide. Our results help to explain the prevalence of pTRM tail-like behavior in paleointensity experiments. They also highlight regions of particles with unusual domain states to target for further investigation into the definitive mechanism behind paleointensity failure.

The ability of rocks to hold a reliable record of the ancient geomagnetic field depends on the structure and stability of magnetic domain-states contained within the rock’s magnetic particles. In paleomagnetic studies, the Day plot is an easily constructed graph of magnetic hysteresis parameters that is frequently used (and mis-used) to estimate the likely magnetic recording stability of samples. Often samples plot in the region of the Day plot attributed to so-called pseudo-single-domain (PSD) particles with little under standing of the implications for domain-states or recording fidelity. Here we use micromagnetic models to explore the hysteresis parameters of magnetite particles with idealized prolate and oblate truncated-octahedral geometries containing single domain (SD), single-vortex (SV) and occasionally multi-vortex (MV) states. We show that these do main states exhibit a well-defined trend in the Day plot that extends from the SD region well into the multi-domain (MD) region, all of which are likely to be stable remanence carriers. We suggest that although the interpretation of the Day plot and its vari33 ants might be subject to ambiguities, if the magnetic mineralogy is known, it can still provide some useful insights about paleomagnetic specimens’ dominant domain state, average particle sizes and, consequently, their paleomagnetic stability.

Quantifying the contributions of distinct mineral populations in bulk magnetic experiments greatly enhances the analysis of environmental and rock magnetism studies. Here we develop a new method of parametric unmixing of susceptibility components in hysteresis loops. Our approach is based on a modified Gamma-Cauchy exponential model, that accounts for variable skewness and kurtosis. The robustness of the model is tested with synthetic curves that examine the effects of noise, sampling, and proximity of susceptibility components. We provide a Python-based script, the Hist-unmix package, which allows the user to adjust a direct model of up to three ferromagnetic components as well as a dia/paramagnetic contribution. Optimization of all the parameters is achieved through least squares fit (Levenberg-Marquardt method), with uncertainties of each inverted parameter calculated through a Monte Carlo error propagation approach. For each ferromagnetic component, it is possible to estimate the magnetization saturation (Ms), magnetization saturation of remanence (Mrs) and the mean coercivity (Bc). Finally, Hist-unmix was applied to a set of weakly magnetic carbonate rocks from Brazil, which typically show distorted hysteresis cycles (wasp-waisted and potbellied loops). For these samples, we resolved two components with distinct coercivities. These results are corroborated by previous experimental data, showing that the lower branch of magnetic hysteresis can be modeled by the presented approach and might offer important mineralogical information for rock magnetic and paleomagnetic studies.

Iron meteorites are believed to be fragments of mantle-stripped planetary cores ejected during catastrophic collisions. They are, therefore, a unique class of material, as they constitute the only available samples from planetary cores. An increasing amount of evidence suggests that the tetrataenite-bearing cloudy zones (CZ) in iron and stony-iron meteorites can preserve magnetic records of ancient magnetic activity of their parent bodies over solar system timescales. Tetrataenite islands in the CZ are nanometer-sized ($<$ 200 nm) crystals that form through ordering from precursor taenite islands upon extremely slow cooling through 320 \textsuperscript{o}C. Recent micromagnetic models have shown that such precursor taenite islands form highly thermally stable single-domain (SD) or single-vortex states (SV). In this work we employ a 3D finite-element multi-phase micromagnetic modeling to show that tetratenite inherits the magnetic remanence of taenite precursor when it forms over underlying SD states. When taenite form SV states, nevertheless, tetrataenite reset the precursor magnetization and record a new remanence through chemical ordering at 320 \textsuperscript{o}C. We further assess the thermal stability of tetrataenite islands. We show that in cases where tetrataenite inherits the domain states of its precursor taenite, the origin of the remanence is in fact 10\textsuperscript{5} years older than in cases where tetrataenite resets the precursor SV magnetization, corresponding to records of two very different stages of planetary formation.

Carbonate rocks frequently undergo remagnetisation events, which can partially/completely erase their primary detrital remanence and introduce a secondary component through thermoviscous and/or chemical processes. Despite belonging to different basins hundreds of kilometres apart, the Neoproterozoic carbonate rocks of South America (over the Amazon and São Francisco cratons) exhibit a statistically indistinguishable single-polarity characteristic direction carried by monoclinic pyrrhotite and magnetite, with paleomagnetic poles far from an expected detrital remanence. We use a combination of classical rock magnetic properties and micro-to-nanoscale imaging/chemical analysis using synchrotron radiation to examine thin sections of these remagnetised carbonate rocks. Magnetic data shows that most of our samples failed to present anomalous hysteresis properties, usually referred to as part of the “fingerprints” of carbonate remagnetisation. Combining scanning electron microscopy-energy-dispersive X-ray spectroscopy (SEM-EDS), highly sensitive X-ray fluorescence (XRF), and X-ray absorption spectroscopy (XAS) revealed the presence of subhedral/anhedral magnetite, or spherical grains with a core-shell structure of magnetite surrounded by maghemite. These grains are within the pseudo-single domain size range (as well as most of the iron sulphides) and spatially associated with potassium-bearing aluminium silicates. Although fluid percolation and organic matter maturation might play an important role, smectite-illitisation seems a crucial factor controlling the growth of these phases. X-ray diffraction analysis identifies these silicates as predominantly highly crystalline illite, suggesting exposure to epizone temperatures. Therefore, we suggest that the remanence of these rocks should have been thermally reset during the final Gondwana assembly, and locked in a successive cooling event during the Early-Middle Ordovician.

Paleomagnetic studies of meteorites constrain the evolution of magnetic fields in the early solar system. These studies rely on the identification of magnetic minerals that can retain stable magnetizations over ≳4.5 billion years (Ga). The ferromagnetic mineral tetrataenite (γ’-Fe0.5Ni0.5) is found in iron, stony-iron and chondrite meteorite groups. Nanoscale intergrowths of magnetostatically-interacting tetrataenite have been shown to carry records of paleomagnetic fields. Tetrataenite can also occur as isolated, non-interacting grains in many meteorite groups. Here we study non-interacting tetrataenite to establish the grain size range over which it can retain magnetization that is stable over solar system history. We present the results of analytical calculations and micromagnetic modelling of isolated tetrataenite grains with various sizes and geometries. We find that tetrataenite forms a stable single domain state for grain lengths between ~10 and 160 nm dependent on its axial ratio. It also possesses a magnetization resistant to viscous remagnetization over the lifetime of the solar system at 293 K. At smaller grain sizes, tetrataenite is superparamagnetic while at larger grain sizes, tetrataenite’s lowest energy state is a lamellar two-domain state that is stable over Ga-scale timescales. Unlike many other ferromagnetic minerals, tetrataenite does not form a single-vortex domain state due to its large uniaxial anisotropy. Our results show that both single domain and two-domain tetrataenite carry extremely stable magnetization and therefore are promising for paleomagnetic studies.